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Notes on Functional Analysis
Rajendra Bhatia, Indian Statistical Institute, New Delhi, India
A publication of Hindustan Book Agency.
Hindustan Book Agency
2009; 248 pp; hardcover
ISBN-10: 81-85931-89-5
ISBN-13: 978-81-85931-89-0
List Price: US$44
Member Price: US$35.20
Order Code: HIN/38
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These notes are a record of a one-semester course on Functional Analysis given by the author to second-year Master of Statistics students at the Indian Statistical Institute, New Delhi. Students taking this course have a strong background in real analysis, linear algebra, measure theory and probability, and the course proceeds rapidly from the definition of a normed linear space to the spectral theorem for bounded selfadjoint operators in a Hilbert space.

The book is organized as twenty-six lectures, each corresponding to a ninety-minute class session. This may be helpful to teachers planning a course on this topic. Well-prepared students can read it on their own.

A publication of Hindustan Book Agency; distributed within the Americas by the American Mathematical Society. Maximum discount of 20% for all commercial channels.

Readership

Graduate students and research mathematicians interested in functional analysis.

Table of Contents

  • Banach spaces
  • Dimensionality
  • New Banach Spaces from old
  • The Hahn-Banach theorem
  • The uniform boundedness principle
  • The open mapping theorem
  • Dual spaces
  • Some applications
  • The weak topology
  • The second dual and the weak* topology
  • Hilbert spaces
  • Orthonormal bases
  • Linear operators
  • Adjoint operators
  • Some special operators in Hilbert space
  • The resolvent and the spectrum
  • Subdivision of the spectrum
  • Spectra of normal operators
  • Square roots and the polar decomposition
  • Compact operators
  • The spectrum of a compact operator
  • Compact operators and invariant subspaces
  • Trace ideals
  • The spectral theorem-I
  • The spectral theorem-II
  • The spectral theorem-III
  • Index
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